Research Article

Analysis of vector concept understanding and its correlation with basic mathematical abilities of prospective science teachers

Ogi Danika Pranata 1 *
More Detail
1 IAIN Kerinci, Sungai Penuh, INDONESIA* Corresponding Author
Contemporary Mathematics and Science Education, 6(1), January 2025, ep25001, https://doi.org/10.30935/conmaths/15723
Submitted: 21 September 2024, Published Online: 14 December 2024, Published: 01 January 2025
OPEN ACCESS   54 Views   37 Downloads
Download Full Text (PDF)

ABSTRACT

This study investigates the relationship between basic mathematical skills and the understanding of vector concepts among 54 prospective science teachers enrolled in basic physics and basic math courses. The research employed a descriptive and correlational quantitative approach, utilizing data from vector tests and basic mathematics assessments administered during the courses. Descriptive statistical analyses revealed that participants showed varying levels of proficiency in both vector understanding and basic mathematical abilities, with average scores indicating a moderate level of competence overall. Correlational analysis using Pearson correlation coefficients found a significant positive relationship (r=0.477, ρ=0.001 ) between basic mathematical skills and the understanding of vector concepts, suggesting that higher proficiency in basic mathematical skills corresponds to better understanding of vector concepts. Further analysis segmented by dimensions of vector operations indicated stronger correlations in two-dimensional vector understanding (r=0.503, ρ=0.000 ) compared to one-dimensional operations (r=0.348, ρ=0.014 ). Basic geometry emerged as the most influential predictor of understanding of vector concepts, exhibiting the highest correlation with both overall understanding of vector concepts (r=0.444, ρ=0.001 ) and 2D understanding of vector concepts (r=0.430, ρ=0.0021 ). These findings underscore the critical role of mathematical competence, particularly in geometric reasoning, in facilitating conceptual understanding in physics education. In conclusion, strengthening basic mathematics skills among prospective science teachers is essential for enhancing their ability to teach and understand physics, particularly in topics like vectors. Future research should explore instructional strategies to address gaps in math-physics integration.
Keywords: basic mathematical skills, conceptual understanding, correlation, physics, vector

CITATION (APA)

Pranata, O. D. (2025). Analysis of vector concept understanding and its correlation with basic mathematical abilities of prospective science teachers. Contemporary Mathematics and Science Education, 6(1), ep25001. https://doi.org/10.30935/conmaths/15723

REFERENCES

  1. Arons, A. B. (1997). Teaching introductory physics. John Wiley & Sons. https://doi.org/10.1063/1.881810
  2. Barniol, P., & Zavala, G. (2014a). Force, velocity, and work: The effects of different contexts on students’ understanding of vector concepts using isomorphic problems. Physical Review Special Topics–Physics Education Research, 10, Article 020115. https://doi.org/10.1103/PhysRevSTPER.10.020115
  3. Barniol, P., & Zavala, G. (2014b). Test of understanding of vectors: A reliable multiple-choice vector concept test. Physical Review Special Topics–Physics Education Research, 10, Article 010121. https://doi.org/10.1103/PhysRevSTPER.10.010121
  4. Béchard, N., Langlois, S., Poliquin, G., & Cyr, S. (2021). Development of the SMIQ questionnaire measuring interest, sense of self-efficacy and perception of the links existing between mathematics and science in an integrated context. Mesure et Évaluation en Éducation, 44(Spécial), Article 129. https://doi.org/10.7202/1100057ar
  5. Buick, J. M. (2007). Investigating the correlation between mathematical pre-knowledge and learning gains in service physics. European Journal of Physics, 28(6), 1073–1080. https://doi.org/10.1088/0143-0807/28/6/004
  6. Chen, J., Pereira, J., Zhou, Y., Li, X., Tamur, M., & Syaharuddin, S. (2021). Correlation between mathematics and physics achievement of senior high school students. Tarbawi: Jurnal Ilmu Pendidikan, 17(1), 14–26. https://doi.org/10.32939/tarbawi.v17i1.768
  7. Cohen, J. (1988). Statistical power analysis for the behavioral science. Lawrence Erlbaum Associates.
  8. Crowell, B. (2007). Newtonian physics. ATE Central.
  9. de Winter, J., & Hardman, M. (2020). Teaching secondary physics. In J. de Winter, & M. Hardman (Eds.), Teaching secondary science.
  10. Djudin, T. (2023). Transferring of mathematics knowledge into the physics learning to promote students’ problem-solving skills. International Journal of Instruction, 16(4), 231–246. https://doi.org/10.29333/iji.2023.16414a
  11. Hawkins, J. M., Thompson, J. R., Wittmann, M. C., Sayre, E. C., & Frank, B. W. (2010). Students’ responses to different representations of a vector addition question. AIP Conference Proceedings, 1289, 165–168. https://doi.org/10.1063/1.3515188
  12. Heafner, J. (2015). The language of the arrows. The Physics Teacher, 53(7), 445–446. https://doi.org/10.1119/1.4931020
  13. Jensen, J. H., Niss, M., & Jankvist, U. T. (2017). Problem solving in the borderland between mathematics and physics. International Journal of Mathematical Education in Science and Technology, 48(1), 1–15. https://doi.org/10.1080/0020739X.2016.1206979
  14. Kaldaras, L., & Wieman, C. (2023). Cognitive framework for blended mathematical sensemaking in science. International Journal of STEM Education, 10(1). https://doi.org/10.1186/s40594-023-00409-8
  15. Kapucu, S., Öçal, M. F., & Şimşek, M. (2016). Evaluating high school students’ conceptions of the relationship between mathematics and physics: Development of a questionnaire. Science Education International, 27(2), 253–276.
  16. Knight, R. D. (1995). The vector knowledge of beginning physics students. The Physics Teacher, 33(2), 74–77. https://doi.org/10.1119/1.2344143
  17. Kuo, E., Hull, M. M., Elby, A., & Gupta, A. (2020). Assessing mathematical sensemaking in physics through calculation-concept crossover. Physical Review Physics Education Research, 16(2), Article 020109. https://doi.org/10.1103/PhysRevPhysEducRes.16.020109
  18. Leech, N. L., Barret, K. C., & Morgan, G. A. (2005). SPSS for intermediate statistics. Use and interpretation. Lawrence Erlbaum Associates, Inc.
  19. Liu, P. H., & Liu, S. Y. (2011). A cross-subject investigation of college students’ epistemological beliefs of physics and mathematics. Asia-Pacific Education Researcher, 20(2), 336–351.
  20. Meli, K., Zacharos, K., & Koliopoulos, D. (2016). The integration of mathematics in physics problem solving: A case study of Greek upper secondary school students. Canadian Journal of Science, Mathematics and Technology Education, 16(1), 48–63. https://doi.org/10.1080/14926156.2015.1119335
  21. Meltzer, D. E. (2002). The relationship between mathematics preparation and conceptual learning gains in physics: A possible “hidden variable” in diagnostic pretest scores. American Journal of Physics, 70(12), 1259–1268. https://doi.org/10.1119/1.1514215
  22. Michelsen, C. (2005). Expanding the domain–Variables and functions in an interdisciplinary context between mathematics and physics. In Proceedings of the 1st International Symposium of Mathematics and Its Connections to the Arts and Sciencies (pp. 201–214).
  23. Michelsen, C. (2015). Mathematical modeling is also physics–Interdisciplinary teaching between mathematics and physics in Danish upper secondary education. Physics Education, 50(4), 489–494. https://doi.org/10.1088/0031-9120/50/4/489
  24. Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barret, K. C. (2004). SPSS for introductory statistics. Use and interpretation. Lawrence Erlbaum Associates, Inc. https://doi.org/10.4324/9781410610539
  25. National Research Council. (2012). A framework for K-12 science education: Practices, crosscutting concepts, and core ideas. The National Academies Press.
  26. Neumann, I., Sorge, S., Hoth, J., Lindmeier, A., Neumann, K., Heinze, A., Neumann, I., Sorge, S., Hoth, J., & Lindmeier, A. (2021). Studies in higher education synergy effects in learning? The influence of mathematics as a second subject on teacher students’ physics content knowledge. Studies in Higher Education, 46(10), 2035–2046. https://doi.org/10.1080/03075079.2021.1953335
  27. Pranata, O. D. (2023). Physics education technology (PhET) as confirmatory tools in learning physics. Jurnal Riset Fisika Edukasi dan Sains, 10(1), 29–35. https://doi.org/10.22202/jrfes.2023.v10i1.6815
  28. Pranata, O. D. (2024). Students’ understanding of vector operations: With and without physics education technology simulation. Journal of Mathematics and Science Teacher, 4(3), Article em068. https://doi.org/10.29333/mathsciteacher/14633
  29. Pranata, O. D., & Lorita, E. (2023). Analisis korelasi kemampuan berbahasa panah dengan kualitas free-body diagram siswa pada materi dinamika [Correlation analysis of arrow language skills with the quality of students’ free-body diagrams on dynamics material]. Jurnal Pendidikan Fisika dan Sains, 6(1), 22–31. https://doi.org/10.52188/jpfs.v6i1.394
  30. Pranata, O. D., & Seprianto, S. (2023). Pemahaman konsep siswa melalui skema blended learning menggunakan lembar kerja berbasis simulasi [Students’ conceptual understanding through a blended learning scheme using simulation-based worksheets]. Karst: Jurnal Pendidikan Fisika Dan Terapannya, 6(1), 8–17. https://doi.org/10.46918/karst.v6i1.1724
  31. Pranata, O. D., Wartono, W., & Yuliati, L. (2016). Kesulitan siswa SMA pada penggunaan free-body diagram dalam materi dinamika [High school students’ difficulties in using free-body diagrams in dynamics material]. In Proceedings of the National Seminar on Postgraduate Science Education UM (pp. 394–404).
  32. Pranata, O. D., Yuliati, L., & Wartono. (2017). Concept acquisition of rotational dynamics by interactive demonstration and free-body diagram. Journal of Education and Learning, 11(3), 291–298. https://doi.org/10.11591/edulearn.v11i3.6410
  33. Putri, D. H., & Pranata, O. D. (2023). Eksplorasi kejenuhan siswa dalam pembelajaran sains setelah pandemi [Exploring student boredom in science learning after the pandemic]. Jurnal Inovasi Pendidikan Sains, 4(2), 62–70. https://doi.org/10.37729/jips.v4i2.3367
  34. Shaffer, P. S., & McDermott, L. C. (2005). A research-based approach to improving student understanding of the vector nature of kinematical concepts. American Journal of Physics, 73(10), 921–931. https://doi.org/10.1119/1.2000976
  35. Ulandari, S., Pranata, O. D., & Kencanawati, I. (2024). Analisis minat siswa dalam konteks integratif: Studi deskriptif dan komparatif dalam [Analysis of students’ interests in an integrative context: A descriptive and comparative study in]. Jurnal Pendidikan MIPA, 14(1), 131–138. https://doi.org/10.37630/jpm.v14i1.1486
  36. Wilson, M. (2014). Student and expert perceptions of the role of mathematics within physics. Waikato Journal of Education, 19(2). https://doi.org/10.15663/wje.v19i2.101
  37. Zhao, F. F., & Schuchardt, A. (2021). Development of the sci-math sensemaking framework: Categorizing sensemaking of mathematical equations in science. International Journal of STEM Education, 8(1). https://doi.org/10.1186/s40594-020-00264-x